If you have 25.4 (or was it 25.3?) or later, you have all the functionality of Dolet 7 and Dolet 8 for Sibelius that adds .mxml v.4.

No, MusicXML is not broken (that I know of). There are a number of things of which you need to be aware. Please describe the exact steps you are taking. Screen shots help such as this one from Preferences:

The steps I have taken are described above ... It worked perfectly in 2014.5, from which I have recently upgraded to 27.1 (don't have 2014.5 on the computer anymore). And like I also said, it works fine with exporting individual files, but it doesn't work when attempting to translate a whole folder.

These are the settings used -

I choose TranslateI Folder to XML, I then choose a Finale files folder, OK, which brings up a screen saying that existing XML files will be replaced, I OK to continue - nothing whatsoever happens

Let's look at this. Why v.4 compressed? What happens when you try Export uncompressed? How about 3.1 or 3.0? 

Why are you exporting folders? Archive? Get them to a publisher or other user? Other? 

There's more info here:

https://usermanuals.finalemusic.com/FinaleWin/Content/Finale/sub-export.htm?Highlight=export%20folder%20musicxml 

Let's be clear. I'm not saying there isn't a problem; it's working for me. Use the Submit a request link at the top of the page to send this to MM Support. That form will want more info than I'm asking.

To update - I have been discussing this with Finale Support, who have so far not come up with a solution (and no, recreating your preferences does nothing here). However .... In Finale scripts there exists a script under Batch Process > Batch Export Music XML, and that works! You have to set the source and destination folders first in Finale Script Options. It converts all files in the chosen folder to the settings you have made in Export > MusicXML Preferences.

Of course by now I've done what I had to do by converting files individually, but it's nevertheless good to know. Why it doesn't work from the Export menu (as it is intended to) is still a mystery, though.

Having had input (on the other forum) from MusicXML directly - here their final and, having tested it again, correct answer:  

I think we have figured out the problem. MusicXML batch export was relying on the presence of short 8.3 file names on Windows to search for all the .mus and .musx files together in a folder. However, some newer PCs don't use short 8.3 file names, so this no longer works on those systems. It would only work if you have a folder with .mus files rather than .musx files.

Translate Folder to MusicXML now works in Finale 27.2, but it looks like it just invokes the Finale Script Batch Export feature, as I had noted before

using the Finale Script, it actually opens every single .mus file in that folder while translating them.

If one transates a folder with many files in it, that's a lot of open Finale files. Is that really intentional or, rather, necessary?

It's not invoking the FinaleScript batch export feature, but it is doing something similar. You have to have a Finale file open to export it, so yes, there will be a lot of Finale files opened during the process in large folders. Each file should close after its export finishes.

Right you are. I tested Translate Folder to MusicXML again and all files in a folder (any chosen folder, actually, not necessarily the folder of the one open file) get translated and are closed. Great! Works perfectly now. (I guess for some reason I had assumed it invoked the Finale batch script, where the files indeed stay open - sorry)

I get Access Denied  for MUS files when using the batch Translate folder to MusicXML. It works fine for MUSX files. Any idea why it works for one and not the other. I have same XML settings as the first screen capture above. Thanks.

.mus files were created by a number of applications. Otherwise, we need more info. Mac or Windows and OS?

If it’s not a huge number of files, open them with Finale 25 or later and save — this will default to .musx.